Question: Simplify to lowest terms. $\dfrac{28}{36}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 28 and 36? $28 = 2\cdot2\cdot7$ $36 = 2\cdot2\cdot3\cdot3$ $\mbox{GCD}(28, 36) = 2\cdot2 = 4$ $\dfrac{28}{36} = \dfrac{7 \cdot 4}{ 9\cdot 4}$ $\hphantom{\dfrac{28}{36}} = \dfrac{7}{9} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{28}{36}} = \dfrac{7}{9} \cdot 1$ $\hphantom{\dfrac{28}{36}} = \dfrac{7}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{28}{36}= \dfrac{2\cdot14}{2\cdot18}= \dfrac{2\cdot 2\cdot7}{2\cdot 2\cdot9}= \dfrac{7}{9}$